engUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332014-10-01242052153138Existence and uniqueness of solutions for p-laplacian fractional order boundary value problemsRahmat Ali Khanrahmat_alipk@yahoo.com1Aziz Khanazizkhan927@yahoo.com2Department of Mathematics, University of Malaknd at Chakdara Dir Lower, Khybar Pakhtunkhwa, PakistanUniversity of Peshawar, PakistanIn this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.http://cmde.tabrizu.ac.ir/article_3138_d0d51e21fca62f083313ef3d8e8382a6.pdfFractional differential equationsThree point boundary conditionsFixed point theoremsp-Laplacian operatorengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332014-10-01242162263316The B"{a}cklund transformation method of Riccati equation to coupled Higgs field and Hamiltonian amplitude equationsAhmad Hasan Arnousahmed.h.arnous@gmail.com1Mohammad Mirzazadehmirzazadehs2@guilan.ac.ir2Mostafa Eslamimostafa.eslami@umz.ac.ir3Department of Engineering Mathematics and Physics, Higher Institute of Engineering, El Shorouk, Cairo, EgyptDepartment of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranIn this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathematical physics and engineering sciences. Obtained solutions may also be important of significance for the explanation of some practical physical problems.http://cmde.tabrizu.ac.ir/article_3316_ee955e00f9d31c2df0030b5e9eb6adc2.pdfComplex nonlinear wave equationsexact solutionsB"{a}cklund transformation method of Riccati equationengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332014-10-01242272423169Topological soliton solutions of the some nonlinear partial differential equationsOzkan Gunerozkanguner@karatekin.edu.tr1Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri-TURKEYIn this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note that, this method is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.http://cmde.tabrizu.ac.ir/article_3169_3e9ca9ba1422f83c2e9e20459cfdf8e4.pdfExact solutiontopological soliton solutionthe (3+1)-dimensional shallow water wave equationthe symmetric regularized long wave (SRLW) equationengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332014-10-01242432553772Generalized B-spline functions ‎method‎‎ for solving optimal control problemsYousef Edrisi Tabrizyedrisy@gmail.com1Aghileh Heydaria_heidari@pnu.ac.ir2Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, IranDepartment of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran‎In this paper we introduce a numerical approach that solves optimal control problems (OCPs)‎‎using collocation methods‎. ‎This approach is based upon B-spline functions‎.‎The derivative matrices between any two families of B-spline functions are utilized to‎‎reduce the solution of OCPs to the solution of nonlinear optimization problems‎.‎Numerical experiments confirm our theoretical findings‎.http://cmde.tabrizu.ac.ir/article_3772_469ce62234092e58427d577e03b4b0d4.pdfOptimal control problem‎‎B-spline functions‎‎Derivative matrix‎‎Collocation methodengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332014-10-01242562673583Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equationsMohammad Mehdizadeh Khalsaraeimuhammad.mehdizadeh@gmail.com1Reza Shokri Jahandizireza.shokri.j@gmail.com2Faculty of Mathematical Science, University of Maragheh, Maragheh, IranFaculty of Mathematical Science, University of Maragheh, Maragheh, IranSystems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawbacks such as spurious oscillations and negative solutions because of truncation errors and may then become unstable. we propose a new scheme that guarantees a smooth numerical solution, free of spurious oscillations and satisfies the positivity requirement, as is demanded for the advection-diffusion reaction equations. The method is applicable to both advection and diffusion dominated problems. We give some examples from different applications.http://cmde.tabrizu.ac.ir/article_3583_bfed57f3653505f17e60608b463669be.pdfNonstandard finite differencespositivityAdvection-diffusion reaction equationM-matrixengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332014-10-01242682823834Fractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equationsMohammadreza Ahmadi Daraniahmadi.darani@sci.sku.ac.ir1Shirin Bagherishirinbagheri55@yahoo.com2Faculty of mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran.Faculty of Basic Sciences, Islamic Azad University, Science and Research Branch, P. O. Box 14515/775, Tehran, Iran.The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test problems are discussed at the end of paper to show the efficiency of the proposed method.http://cmde.tabrizu.ac.ir/article_3834_bb3f883a1e0a93f9f79e70f8f6790c93.pdfIntegro-differential equationsfractional type of flatlet oblique multiwaveletsbiorthogonal flatlet multiwavelet system